Air is moving but it isn't cold. That narrows things down more than most people realise — the blower is clearly working, so the problem is almost always in the cooling side rather than the air side.
Before anything else, check the thermostat is actually set to COOL and not FAN. It sounds obvious, and it is genuinely one of the more common causes of a house full of moving, room-temperature air — especially after someone else has touched the thermostat.
Second, look at your filter. A filter packed solid restricts airflow so badly that the system can't move enough air across the coil to cool it properly. If you can't see light through it, replace it.
Third, check the breaker. Many systems run the outdoor unit on a separate breaker from the indoor blower. If that one has tripped, the fan keeps blowing but nothing is being cooled — which is exactly the symptom you're describing. Reset it once. If it trips again, stop and call someone; a breaker that keeps tripping is telling you about a real electrical fault.
If you see frost or ice on the copper lines or the indoor coil, switch the system to OFF and leave the fan running. That sounds backwards, but running the fan without cooling is what thaws the coil, and running the compressor against a frozen coil is what destroys it.
A frozen coil is a symptom, not a cause. It usually means airflow has been restricted long enough for the coil to drop below freezing — a filter, a blocked return, a failing blower — or that the refrigerant charge is low. The first group you can sometimes fix. The second needs a technician, because low refrigerant means there's a leak, and adding more without finding the leak just puts you back here next summer.
Go outside and listen. If the outdoor fan is spinning and you can hear the compressor running, the system is trying. If the fan is still, or you hear a hum without anything turning, that's very often a failed capacitor — a common part, an inexpensive one, and a repair rather than a replacement.
Do not open that cabinet to look. A capacitor stores a charge long after the power is off, and that charge is enough to hurt you badly. This is the point where the honest answer is to call somebody.
If the fan runs but the coil around the outside is packed with dust and cottonwood, that alone can stop the system rejecting heat. In Tucson that happens faster than most people expect. Rinsing it gently from the outside with a garden hose, power off, helps more than it sounds like it should.
An air conditioner doesn't consume refrigerant. If it's low, it leaked, and the leak is the actual repair. Topping a system up without finding the leak is a temporary fix sold as a permanent one — and refrigerant handling is EPA-regulated, so it isn't something to do yourself regardless.
We read pressures on the actual unit before touching anything, because the same warm-air symptom can be a leak, a failing compressor, a bad metering device, or something as simple as a dirty coil. Those have very different price tags and guessing between them is how people end up paying twice.
We're open 24 hours and we diagnose with gauges, not guesses. A service call is $120, or $190 after hours, and you'll know the repair cost before we start.